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On the existence of monotone selections

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Author Info
Kukushkin, Nikolai S.

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Abstract

For a correspondence from a partially ordered set to a lattice, three sets of sufficient conditions for the existence of a monotone selection are obtained. (1) The correspondence is weakly ascending while every value satisfies a completeness condition, e.g., is chain-complete. (2) The correspondence is ascending while the target is a sublattice of the Cartesian product of a finite number of chains. (3) Both source and target are chains while the correspondence is generated by the maximization of a strongly acyclic interval order with the single crossing property. The theorems give new sufficient conditions for the existence of (epsilon) Nash equilibria.

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Publisher Info
Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 14451.

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Date of creation: 20 Jun 2009
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Handle: RePEc:pra:mprapa:14451

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Related research
Keywords: Monotone selection; (weakly) ascending correspondence; interval order; single crossing; (epsilon) Nash equilibrium;

Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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References listed on IDEAS
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  1. Kukushkin, Nikolai S., 2004. "Best response dynamics in finite games with additive aggregation," Games and Economic Behavior, Elsevier, vol. 48(1), pages 94-110, July. [Downloadable!] (restricted)
  2. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
  3. Kukushkin, Nikolai S., 1994. "A fixed-point theorem for decreasing mappings," Economics Letters, Elsevier, vol. 46(1), pages 23-26, September. [Downloadable!] (restricted)
  4. Novshek, William, 1985. "On the Existence of Cournot Equilibrium," Review of Economic Studies, Blackwell Publishing, vol. 52(1), pages 85-98, January. [Downloadable!] (restricted)
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  5. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January. [Downloadable!] (restricted)
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  6. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321. [Downloadable!] (restricted)
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